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numbers and algebraic expressions
logic, sets, intervals
absolute value
function and its properties
linear function
quadratic function
polynomials
rational function
exponential function
logarithm
number sequences
limits of sequences and functions
derivative and integral of functions
trigonometry
plane geometry
analytic geometry
solid geometry
combinatorics
probability
elements of statistics
kropki game

Logarithm. Examples: log_2 8 - logarithm of 8 with base 2. log_4 16 - logarithm of 16 with base 4. log 1000 - common logarithm of 1000 (base equal 10). ln 7 - natural logarithm of 7 (base equal e ≈ 2.718). The logarithm of b with base a: log_a b. Conditions for the base a: a * 0 i a ≠ 1. Conditions for the number b: b * 0. The definition of a logarithm: log_a b = x if a^x = b. Examples: log_2 8 = 3 - because 2^3 = 8. log_4 16 = 2 - because 4^2 = 16. log 1000 = 3 - because 10^3 = 1000.